Math-BridgeEducation Solution

MATH-BRIDGECONTENT COLLECTIONS

Dr. Giorgi Goguadze

A Collection of Pre-recorded courses available at mathbridge.celtech.de

Basic mathematics course• Numbers and basic arithmetic• General, linear and quadratic equations• Linear and quadratic functions

Natural Numbers• Definition of natural numbers, number line • Operations on naturals

• Addition, Multiplication• Illustrative Examples• Interactive Exercises

Integers• Subtraction and negative integers• Operations on integers

• Addition, subtraction, multiplication• Division and factorization

• Order of computations, operation precedence

Rational Numbers• Fractions and Rational Numbers• Reduction of fractions using GCD• Operations with fractions

• Addition, subtraction, multiplication and division, inverses• Combinations of addition and multiplication

• A collection of mixed exercises on fractions

Powers• Powers of positive and negative integers• Powers of fractions, Powers of powers• Operations with powers

• multiplication and division of powers• 1 and 0 as exponents

• A collection of mixed exercises on powers

Roots• Square Root, third root, n-th root• Computations with roots• A collection of exercises

Real Numbers• Square Root of 2, irrational numbers• Sets of numbers• Interval notation• Exercsies

Calculations with letters

• Term manipulation• Handling brackets

General Equations, Linear Equations • Theory, definitions, examples• Interactive Exercises with Domain Reasoners

General Functions, Linear Functions

• Theory, definitions, Value Tables, Graph of Functions• Linear Functions, Slope of Function, Line Equation,

Interception Form• Displacement in x- and y- direction

Quadratic Equations, Quadratic Functions

• Quadratic Formula, Vieta’s Theorem• Parabolas, Displacement and Stretching of Parabola

Exponential Function• Integer exponents, negative exponents• Non-integer exponents• Exponential equation

More Equations and Inequalities

• Higher degree polynomial equations• Rational Equations• Equations with Powers• Quadratic Inequalities

Differentiation

• Intuitive Definition, Slope of a Function, Examples• Exercises on Differentiation of Polynomials• Product Rule, Quotient Rule

Enriched VEMA Content• Calculation Rules

• Field Axioms and Calculation Rules• Inequalities• Number Sets• Arithmetic• Logic and Proof

• Powers• Integer Exponents• Geometric Sequences and Series• Binominal Coefficients• Powers with Rational Exponents

• Functions• Linear Functions• Quadratic Functions• General Functions

• Higher functions• Polynomial Functions, Horners Method• Polynomial Division, Zeros of Polynomials

• Calculus ->

Enriched VEMA Content

• Calculus • Sequences of numbers, Limits of sequences• Limits of Functions and Continuity• Differential Calculus

• Derivatives• Differentiate Polynomials• Differentiation Rules

• Product Rule• Quotient Rule• Chain Rule

• Integral Calculus• Calculating Integrals• Integration by Parts• Substitution• Integration of Rational Functions

Enriched VEMA Content: Didactic Approach

• All course chapters have similar hierarchical structure

School Mathematics: Fractions Course• Didactic Concept• Multimedia Content• Interactive Exercises

School Mathematics: Fractions Course• General Concept and Interpretations• Calculating with Fractions, Examples, Interactive Exercises• Decimal numbers• Assessment tests

IDEAS Exercise Collection

• A large number of exercises on different topics• Flag feedback in every step• Hints and solutions in every step

• To be reused in different collections

Introduction to Calculus

• Former LeActiveMath Calculus Content• Covers University First Year Calculus Content on Differential Calculus

Introduction to Calculus

• Basics• Straight lines (slope, linear equations, intersection angles)• Binomial Formulas• Bounded Sets

• Sequences, Series, and Limits• Limits of Sequences, Bounded Sequences• Computation with Limits• Subsequences, Cauchy Sequences• Series, Convergent and Absolutely Convergent Series• Power Series

• Functions and Relations• Inverse and Composite Relations• Special Relations: Equivalence, (Partial/Well) Orders• Functions, Definitions and Properties (Injective, Surjective)• Roots of functions, Simple Functions• Quadratic, Polynomial, Rational, Step Function• Inverse Functions, Composed Functions• Symmetric, Monotonic, Periodic Functions

Introduction to Calculus• Functions and Relations

• Trigonometric Functions• Limits of Functions• Continuity

• Differential Calculus• Average Slopes, Rates of Change• Difference Quotients• Introduction to Derivatives• Differentiation Rules• Derivatives of Various Functions• Theorems on Differentiable Functions• Applications of Differential Calculus

• Appendix• Extras on Functions, Roots, Gaps in the Domain• Special Properties of Functions, Derivatives of Simple Functions• Differentiation Rules for Sum, Product, Quotient, Chain Rule• Comprehension of Derivatives• Curve Discussion

• On Mathematical Proofs, Induction• Sum Formulae

Short Introduction to Calculus (Demo Content)• Average Slopes• Difference Quotient• Actual Slope• Differential Quotient• Derivative Function• Supplement: Rate of Change• Derivatives of Constant Functions, Derivative of Identity Function

Mathematics Remedial Instruction (TUT Collection)

• Real Numbers• Rational and irrational function• Field Axioms, Order Axioms, Completeness Axioms• Infinity, Number line, Decimal Presentation

• Expressions• Powers, Polynomials• Divisibility, Factors and Roots of Polynomial• Addition, Subtraction, Multiplication and Division of Polynomials• Rational Expressions, Absolute Value • Roots, Rational Powers, General Power

• Functions• Mapping, Properties of Functions• Operations on Functions• Limit of a function, Right and Left Limits• Limit in Infinity, Infinite Limit• Continuity of a Function, Properties of Continuous Function

Mathematics Remedial Instruction (TUT Collection)

• Linear Equations and Inequalities• Trigonometry• General Equations and Inequalities• Logarithm and Exponential Function, Logarithm Equations• Differential Calculus

• Difference Quotient• Derivation Rules• Derivatives of Trigonometric Function• Derivative of Exponential and Logarithmic Function• Extrema of Function • Mean Value Theorems of Differential Calculus• Solving Extremum Applications

• Integral Calculus• Integration Rules• Integral of Composite Function• Integration of Rational Function• Area of a Plane Figure, Definite Integral• Mean Value Theorem of Integral Calculus• Area Bounded by a Curve, Volume of a Body• Infinite Integrals

Repetition of High School Mathematics (Vienna Collection)

• Sets• Numbers• Geometry

• Cartesian Plane and Coordinate System• Analytic Geometry• Vectors• Trigonometry

• Functions• Variables, Terms, Formulas and Identities• Equations, Powers, Exponential Function and Logarithm• Trigonometric Functions

• Differentiation• Definitions• Applications

• Curve Sketching• Extremum, Inflection Points, Minimum, Maximum

• Integration• Probability Theory

• Events and probabilities, Randomness, Stochastic Experiments• Distributions, Standard Deviation, Expectation, Mean Value

Repetition of High School Mathematics (Vienna Collection)

• A lot of useful multimedia Interactive exercises, mostly multiple choice or puzzles

Reusing Math-Bridge Content at Leuphana University in Lüneburg

• Selected content for bridging course

• One Collection corresponds to a Book Chapter

• Selected Learning Objects and Interactive Exercises from different Math-Bridge Collections are merged

• Chapter Sections have similar didactic structure

• Based mostly on VEMA/VEMINT content

• Corresponds to School Mathematics needed for entering a University

Thank you.

The Mathematical Bridge, Cambridge, England